diff --git a/scripts/package/builddeb b/scripts/package/builddeb
index 404587fc71fe..441b0bb66e0d 100755
--- a/scripts/package/builddeb
+++ b/scripts/package/builddeb
@@ -123,7 +123,7 @@ install_kernel_headers () {
 	pdir=debian/$1
 	version=${1#linux-headers-}
 
-	"${srctree}/scripts/package/install-extmod-build" "${pdir}/usr/src/linux-headers-${version}"
+	CC="${DEB_HOST_GNU_TYPE}-gcc" "${srctree}/scripts/package/install-extmod-build" "${pdir}/usr/src/linux-headers-${version}"
 
 	mkdir -p $pdir/lib/modules/$version/
 	ln -s /usr/src/linux-headers-$version $pdir/lib/modules/$version/build
diff --git a/scripts/package/install-extmod-build b/scripts/package/install-extmod-build
index d2c9cacecc0c..7ec1f061a519 100755
--- a/scripts/package/install-extmod-build
+++ b/scripts/package/install-extmod-build
@@ -44,13 +44,11 @@ mkdir -p "${destdir}"
 	fi
 } | tar -c -f - -T - | tar -xf - -C "${destdir}"
 
-# When ${CC} and ${HOSTCC} differ, we are likely cross-compiling. Rebuild host
-# programs using ${CC}. This assumes CC=${CROSS_COMPILE}gcc, which is usually
-# the case for package building. It does not cross-compile when CC=clang.
+# When ${CC} and ${HOSTCC} differ, rebuild host programs using ${CC}.
 #
 # This caters to host programs that participate in Kbuild. objtool and
 # resolve_btfids are out of scope.
-if [ "${CC}" != "${HOSTCC}" ] && is_enabled CONFIG_CC_CAN_LINK; then
+if [ "${CC}" != "${HOSTCC}" ]; then
 	echo "Rebuilding host programs with ${CC}..."
 
 	cat <<-'EOF' >  "${destdir}/Kbuild"
diff --git a/scripts/package/mkdebian b/scripts/package/mkdebian
index 10637d403777..93eb50356ddb 100755
--- a/scripts/package/mkdebian
+++ b/scripts/package/mkdebian
@@ -179,6 +179,8 @@ fi
 
 echo $debarch > debian/arch
 
+host_gnu=$(dpkg-architecture -a "${debarch}" -q DEB_HOST_GNU_TYPE | sed 's/_/-/g')
+
 # Generate a simple changelog template
 cat <<EOF > debian/changelog
 $sourcename ($packageversion) $distribution; urgency=low
@@ -196,7 +198,11 @@ Priority: optional
 Maintainer: $maintainer
 Rules-Requires-Root: no
 Build-Depends: debhelper-compat (= 12)
-Build-Depends-Arch: bc, bison, cpio, flex, kmod, libelf-dev:native, libssl-dev:native, rsync
+Build-Depends-Arch: bc, bison, cpio, flex,
+ gcc-${host_gnu} <!pkg.${sourcename}.nokernelheaders>,
+ kmod, libelf-dev:native,
+ libssl-dev:native, libssl-dev <!pkg.${sourcename}.nokernelheaders>,
+ rsync
 Homepage: https://www.kernel.org/
 
 Package: $packagename-$version
@@ -224,6 +230,7 @@ cat <<EOF >> debian/control
 
 Package: linux-headers-$version
 Architecture: $debarch
+Build-Profiles: <!pkg.${sourcename}.nokernelheaders>
 Description: Linux kernel headers for $version on $debarch
  This package provides kernel header files for $version on $debarch
  .